Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.05" was replaced by "(405/100)". 3 more similar replacement(s)

Step  1  :

            81
 Simplify   ——
            20

Equation at the end of step  1  :

    113    53     81     
  ((——— +  ——) +  ——) +  16
    10     10     20     

Step  2  :

            53
 Simplify   ——
            10

Equation at the end of step  2  :

    113    53     81     
  ((——— +  ——) +  ——) +  16
    10     10     20     

Step  3  :

            113
 Simplify   ———
            10 

Equation at the end of step  3  :

    113    53     81     
  ((——— +  ——) +  ——) +  16
    10     10     20     

Step  4  :

Adding fractions which have a common denominator :

 4.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 113 + 53     83
 ————————  =  ——
    10        5 

Equation at the end of step  4  :

   83    81     
  (—— +  ——) +  16
   5     20     

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       20 

      Least Common Multiple:
      20 

Calculating Multipliers :

 5.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 4

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      83 • 4
   ——————————————————  =   ——————
         L.C.M               20  

   R. Mult. • R. Num.      81
   ——————————————————  =   ——
         L.C.M             20

Adding fractions that have a common denominator :

 5.4       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 83 • 4 + 81     413
 ———————————  =  ———
     20          20 

Equation at the end of step  5  :

  413    
  ——— +  16
  20     

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  20  as the denominator :

          16     16 • 20
    16 =  ——  =  ———————
          1        20   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

 413 + 16 • 20     733
 —————————————  =  ———
      20           20 

Final result :

  733            
  ——— = 36.65000 
  20